The present invention concerns transmissions using encryption by deterministic chaos.
The invention finds one advantageous application in the confidential transmission of information in optical networks.
It also finds an application in the microwave field for encrypting radio communications.
In encryption using chaos, the message is concealed in a chaotic signal, that is to say a signal that fluctuates in a random but deterministic manner. The sender of the message has a chaos generator that is used to conceal the message in clear in a chaotic signal. The receiver has another chaos generator which must be synchronized to the first one to be able to decrypt the message correctly.
The chaos generators of most interest for use in encryption are devices known as xe2x80x9cnon-linear systems with delayxe2x80x9d. They comprise a light source which has a feedback loop formed of a non-linear element and a delay line.
They have the advantage of being simple whilst producing chaos with very large dimensions, that is to say very complex chaos, which enables a very high level of confidentiality to be obtained.
The problem that arises with this type of chaos generator is that the sender and the receiver must be synchronized so that the message can be decrypted in real time. Very few implementations in the optical domain have been described before now.
Patent FR 2 743 459 describes an encryption system using as the sender a chaos generator formed of a wavelength tuneable source and a non-linear wavelength component. The device encrypts a message in the form of chaotic modulation of the wavelength emitted by the light source. The document reports that encryption and decryption are effected by the sender and the receiver using non-linear wavelength elements which must be identical in the sender and in the receiver.
This process has the advantage of being simple to implement but it is difficult to use over long distances (i.e. in systems employing optical fibres) because the same wavelength non-linearities must be conserved between the sender and the receiver over the whole distance.
This condition is not satisfied when the transmission channel is a standard optical fibre. The fibre introduces chromatic dispersion effects which affect the wavelengths transmitted between the sender and the receiver, which makes it difficult to obtain conditions enabling the receiver to decrypt the message.
The solution to the problem of producing chaos that is usable over long distances and of avoiding dispersion problems is to use a chaos generator producing chaotic modulation of the luminous intensity from a monochromatic source. Existing devices, referred to hereinafter as xe2x80x9cintensity chaos generatorsxe2x80x9d, cannot be used in the encryption and decryption process described in the previously mentioned patent FR 2 743 459, however, for reasons that will now be explained.
FIG. 1 shows an intensity chaos generator the effect of which is to produce chaotic modulation of the luminous intensity from the monochromatic source 1, as described by P. Celka in an article entitled xe2x80x9cChaotic synchronization and modulation of nonlinear time-delayed feedback optical systemsxe2x80x9d, IEEE Transactions on Circuits and Systems, 42, 8, pp 455-463, 1995. The source 1 is optically connected to an integrated Mach-Zehnder interferometer 2 whose output intensity P(t) 3 is converted by the photodetector 4 into an electrical signal looped to the control electrodes of the interferometer after passing through a delay line T 5. The reader is also referred to the following documents in which the non-linear energy element is an electro-optical crystal, an acousto-optic crystal or a Michelson or Fabry-Pxc3xa9rot interferometer:
F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker xe2x80x9cBifurcation to chaos in optical bistabilityxe2x80x9d, Phys. Rev. A, 25, 4 pp 2172-2182, 1982;
R. Vallxc3xa9e, C. Delisle xe2x80x9cRoute to chaos in an acousto-optic bistable devicexe2x80x9d, Phys. Rev. A, 31, 4 pp 2390-2396, 1985;
Y. Liu, J. Ohtsubo xe2x80x9cChaos in an active interferometerxe2x80x9d, J. Opt. Soc. Am. B, 9, 2, pp 261-265, 1992;
T. Takizawa, T. Liu, J. Ohtsubo, xe2x80x9cChaos in a feedback Fabry-Pxc3xa9rot interferometerxe2x80x9d, IEEE J. of Quantum Electronics, 30, 2, pp 334-338, 1994.
In all the above systems the non-linear element induces energy non-linearity directly in the light issuing from the source and the chaotic luminous signal obtained in this way is looped, after optical-electrical conversion, via a feedback loop with delay to the source or to the electrodes of the non-linear element. The law of evolution of the intensity produced by all the above systems is different from that of the chaos on which the encryption process described in the previously mentioned patent is based, however, which means that it cannot be transposed to the above systems.
Thus in FIG. 1, the luminous intensity P(t) emitted by the emitter is governed by the following equations:       P    ⁡          (      t      )        =                                          P            0                    ⁡                      [                          1              +                              cos                ⁢                                  xe2x80x83                                ⁢                                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                                    λ                                ⁢                                  xe2x80x83                                ⁢                                  V                  ⁡                                      (                                          t                      -                      T                                        )                                                                        ]                          ⁢                  xe2x80x83                ⁢        and        ⁢                  xe2x80x83                ⁢                  V          ⁡                      (            t            )                              +              τ        ⁢                  xe2x80x83                ⁢                  ⅆ                      ⅆ            t                          ⁢                  xe2x80x83                ⁢                  V          ⁡                      (            t            )                                =          η      ⁢              xe2x80x83            ⁢              P        ⁡                  (          t          )                    
where V(t) is the electrical signal produced by the photodetector, xcex7 is its electrical gain, xcfx84 is the time constant of the feedback loop and xcex is the wavelength of the source.
The above two equations can be combined in the form of a non-linear differential equation with delay which governs the law of evolution of the chaos intensity P(t) produced at the output 3 of the interferometer:                                                         λ                              2                ⁢                                  xe2x80x83                                ⁢                π                                      ⁢                          xe2x80x83                        ⁢                                          cos                                  -                  1                                            ⁡                              [                                                                            P                      ⁡                                              (                        t                        )                                                                                    P                      0                                                        -                  1                                ]                                              +                      τ            ⁢                          xe2x80x83                        ⁢                          ⅆ                              ⅆ                t                                      ⁢                          xe2x80x83                        ⁢                                          cos                                  -                  1                                            ⁡                              [                                                                            P                      ⁡                                              (                        t                        )                                                                                    P                      0                                                        -                  1                                ]                                                    =                  η          ⁢                      xe2x80x83                    ⁢                      P            ⁡                          (                              t                -                T                            )                                                          (        1        )            
The chaos obtained and the equation (1) that governs it are different from the model described in the previously cited patent FR 2 477 459, in which the chaos must obey an equation of the type:                                           P            ⁡                          (              t              )                                +                      τ            ⁢                          xe2x80x83                        ⁢                          ⅆ                              ⅆ                t                                      ⁢                          xe2x80x83                        ⁢                          P              ⁡                              (                t                )                                                    =                  π          ⁡                      [                          A              -                              μ                ⁢                                  xe2x80x83                                ⁢                                  sin                  2                                ⁢                                  {                                      MP                    ⁡                                          (                                              t                        -                        T                                            )                                                        }                                                      ]                                              (        2        )            
This makes it impossible to use the simple encryption method described therein.
A much more complex method that is already known per se can be used.
FIG. 2 shows this solution to the problem of decrypting the chaos governed by equation (1). It is based on the method of synchronizing chaos described by Pecora and Caroll in the document xe2x80x9cSynchronization in chaotic systemsxe2x80x9d published in Physical Review Letters, vol. 64, pp 821-824 in 1990. The sender 6 is a chaos generator formed of two coupled sub-systems, a master chaos generator 7 and a slave chaos generator 8. The master generator generates chaos as shown to control the chaos from the slave generator. The message s(t) to be encrypted is encoded (generally in the form of a simple addition) on the slave chaos which behaves like interference noise. The combination is transmitted to the receiver 9. This includes a slave generator 10 (identical to the slave generator of the sender), controlled by the synchronization signal from the master generator of the sender. When the chaos from each generator has been synchronized, the message s(t) can be recovered by subtraction. Note that this method generally necessitates two transmission channels 11 and 12, one for the encrypted signal and the other for the synchronization signal.
One embodiment in the optical domain is described by P. Celka in the previously cited article xe2x80x9cChaotic synchronization and modulation of nonlinear time-delayed systemsxe2x80x9d published in IEEE Transactions on Circuits and Systems, vol. 42, number 8, pp 455-463 (August 1995). The device uses a monochromatic light source and a plurality of Mach-Zehnder interferometers controlled by feedback loops with delay to obtain synchronization between chaos generated by the sender and by the receiver.
FIG. 3 shows the encryption and decryption system proposed in the above article and provides a basis for some explanation of its operating principle. The sender 13 comprises two coupled chaos generators 14, 15 based on the principle shown in FIG. 1. The receiver 16 comprises two modules 17 and 18, each of which comprises two chaos generators 19, 20 and 21, 22 appropriately paired to assure synchronization. Each chaos generator consists of a Mach-Zehnder interferometer the optical output of which is looped electrically to the control electrodes by a feedback loop with delay, as in the embodiment shown in FIG. 1. The reader is referred to basic equations 1 to 4 and to FIGS. 1, 2, 6 and 12 of the article by P. Celka for a complete description of the system and its use for encryption of digital signals by Chaos Shift Keying (CSK).
The devices described above have drawbacks:
In the case of the device described in patent FR 2 743 459, the technical problem arises from the difficulty of complying strictly with the wavelength conditions between the sender and the receiver for large transmission distances using the optical fibres employed in telecommunications (because of their chromatic dispersion). To solve this problem it is necessary to use offset dispersion fibres, but this solution rules out the use of most existing networks.
Existing intensity chaos encryption systems are chaos generators with conditions of use that lead to very complex and costly systems. This complexity leads in particular to major technical difficulties in implementing systems having low time constants suited to high encryption speeds, compatible with the bit rates of several Gbit/s typical of fibre optic telecommunications. Also, in some cases, the Pecora and Caroll method necessitates an additional transmission channel for synchronization, which is a disadvantage in the telecommunication field.
The aim of the present invention is precisely to remedy these drawbacks.
The invention proposes a device for sending an encrypted signal, including a source for generating said signal and means for intensity modulating the signal, a feedback loop which includes delay line means and non-linear means, characterized in that the feedback loop includes an interferometer to which is applied an electric current that corresponds to the delayed generated signal and an auxiliary source of constant intensity that feeds the interferometer optically, the output signal of the interferometer being a non-linear function of the output signal of the delay line means, a photodiode which converts the luminous power at the output of the interferometer to a modulation current, and a summing circuit which adds the message to be encrypted to the modulation current at the output of said photodiode, the output signal of the summing circuit controlling modulator means.
The source for generating the signal is advantageously an optical source, said device including a photodiode which converts the generated signal into an electrical signal and means for injecting the electrical signal into the input of the delay line means.
However, the sender device proposed by the invention can equally be used to send encrypted radio frequency signals, the source for generating the signal then being a radio frequency source.
The invention also proposes a device for receiving an encrypted signal, including means for receiving said signal, a feedback loop which includes delay line means and non-linear means, characterized in that the feedback loop includes an interferometer to which is applied a current that corresponds to the delayed received signal and an auxiliary source of constant intensity which feeds the interferometer optically, the interferometer output signal being a non-linear function of the output signal of the delay line means, a photodiode which converts the luminous power at the interferometer output into a current, and a subtractor circuit which applies the subtraction operation to the received signal and to the output current of said photodiode, the output signal of the subtractor circuit being the demodulated signal.
When the encrypted signal is an optical signal, the receiver means comprise a photodiode that converts the luminous power from the transmission channel into an electrical signal.
When the encrypted signal is a radio frequency signal, the receiver means include a receive antenna.
In a sender or receiver device of the type proposed by the invention, the interferometer is advantageously of the Mach-Zehnder type.
The Mach-Zehnder interferometer is preferably integrated on lithium niobate, gallium arsenide or silicon.